Student Answers
(Answers from Mandy, Elizabeth, and Emily)
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Teacher Answers
39. TRUE - Inverse functions simply
switch their x- and y-values. Also,
since the original function is one-
to-one, its inverse will be a function.
Correct
40. TRUE - For example, plug in the
values of 1 and 2 for "t" to get two
ordered pairs. Plug in 1 for (t+1,2t+3)
and get (2,5). Plug in 2 and get (3,7).
Find the slope by using the
(y2-y1) / (x2-x1) equation -->
(7-5) / (3-2) = 2 / 1 = 2
Correct - nice explanation ...
also - if you eliminate the parameter "t"
you will obtain the equation y=2x+1
41. E - the inverse of answer E (which
is the answer to the original problem)
is (-2,1). Confirmed by plugging the
x- and y-values into the equation
x²y+5y=9. You find the inverse of
that by switching x and y, giving you
an ordered pair of (1,-2). Thus, you end
up with answer E.
Correct
42. B - Original equation is xy² - 3x=12.
Condense it to get x(y²-3)=12. Switch
x and y for the inverse, and plug in the
values. 1(4²-3)=12-->13=12. [false]
Correct
43. C - switch x and y and solve for y.
original: f(x)=3x-2
--> x=3y-2 --> ((x-2)/3)=y
Correct
44. A - switch x and y and solve for y.
orginal: f(x)=x³+1
--> x=y³+1 --> x-1=y³ -->
y=[cube root of (x-1)]
Correct - nice explanations for ALL of these answers!
(Answers from Mandy, Elizabeth, and Emily)
switch their x- and y-values. Also,
since the original function is one-
to-one, its inverse will be a function.
values of 1 and 2 for "t" to get two
ordered pairs. Plug in 1 for (t+1,2t+3)
and get (2,5). Plug in 2 and get (3,7).
Find the slope by using the
(y2-y1) / (x2-x1) equation -->
(7-5) / (3-2) = 2 / 1 = 2
also - if you eliminate the parameter "t"
you will obtain the equation y=2x+1
is the answer to the original problem)
is (-2,1). Confirmed by plugging the
x- and y-values into the equation
x²y+5y=9. You find the inverse of
that by switching x and y, giving you
an ordered pair of (1,-2). Thus, you end
up with answer E.
Condense it to get x(y²-3)=12. Switch
x and y for the inverse, and plug in the
values. 1(4²-3)=12-->13=12. [false]
original: f(x)=3x-2
--> x=3y-2 --> ((x-2)/3)=y
orginal: f(x)=x³+1
--> x=y³+1 --> x-1=y³ -->
y=[cube root of (x-1)]